There is a limit to how long Oak or other hardwood can last in storage conditions. Most of my experience has to do with Oak and Pine. Here in California we have Oak, Cedar, White Fir, Pine, and Eucalyptus in the valley. All the mentioned wood have a great shelf life provided that the wood are kept at 15%. Oak is surprisingly vulnerable to infestation. It will attract insect infestation at 2 years and older even though it is kept relatively dry.
From what I know about Kentucky and its climate you have seasons of very moist weather. It looks like you are using the resources that you have available. Your home made storage shed is probably the best in that air is able to flow around your wood effectively, but after 5 years it could start to decompose. Something that seems to work for me when trying to protect certain wood from decay are mothballs. They last a long time and chemicals do not need to be applied ever couple of months. They work well when the wood is very dry and then partially covered with plastic. Thanks